Analytical calculation of neighborhood order probabilities for high dimensional Poissonic processes and mean field models

Simple item page
dc.creatorTercariol, Cesar Augusto Sangaletti
dc.creatorKiipper, Felipe de Mouta
dc.creatorMartinez, Alexandre Souto
dc.date2006-09-08
dc.date.accessioned2026-07-07T07:50:34Z
dc.date.available2026-07-07T07:50:34Z
dc.descriptionConsider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest neighbor (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality $d$. In the limit $d \to \infty$, the distances between pair of points become indenpendent (random link model) and closed analytical forms for the neighborhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbor or not.
dc.description12 pages, 3 figures and 1 table
dc.identifierhttps://arxiv.org/abs/cond-mat/0609210
dc.identifierhttp://arxiv.org/abs/cond-mat/0609210
dc.identifierJ. Phys. A: Math. Theor. 40 1981--1989 (2007)
dc.identifierdoi:10.1088/1751-8113/40/9/005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125205
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleAnalytical calculation of neighborhood order probabilities for high dimensional Poissonic processes and mean field models
dc.typetext

Files

Collections

arXiv